Clarify the piece shapes and grid representation, then simulate the placement process by scanning each piece's possible anchor positions in row-major order. For each anchor, check if the piece fits without overlapping existing blocks or going out of bounds; if so, place it and move to the next piece, otherwise continue scanning. If no valid anchor is found for a piece, stop and return the current grid.
Pro tip: Precompute each piece's occupied cells relative to its top-left anchor to avoid repeated shape calculations, and consider using bitmasks for efficient collision checks if the grid is large.
Ask about the exact shapes of pieces A-E, grid dimensions, and whether pieces can be placed on occupied cells. Confirm that scanning is top-to-bottom then left-to-right for each piece independently.
Choose a data structure for the grid (e.g., 2D array or bitmask) and define each piece as a list of relative coordinates from its top-left anchor.
For each piece in sequence, iterate over all possible anchor positions in row-major order. For each anchor, check if the piece fits (no out-of-bounds and no overlap). Place at the first valid anchor and break; if none, stop the simulation.
After processing all pieces or stopping early, return the grid state, ensuring it reflects all placed pieces.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Classic union-find or interval merge problem.
Use a hash map to track the lengths of contiguous built segments, updating the lengths of the segments adjacent to each new build. After each build, maintain the maximum segment length seen so far, which only increases, so you can output it in O(1) time.
Pro tip: Emphasize that coordinates can be in the billions, so an array-based approach is infeasible; a hash map keyed by coordinate is necessary. Also, note that the maximum segment length is monotonic, so you can avoid scanning all segments each time.
Confirm that builds are given one by one, and after each build we need to output the current longest contiguous segment of built positions. Ask if positions can be built multiple times (assume no).
Use a hash map (dictionary) to store the length of the contiguous segment for each endpoint of that segment. Also keep a variable for the global maximum segment length.
For a new position x, check if x-1 and x+1 are already built. Compute the new segment length by combining left and right segments (if any) plus 1. Update the length for the new segment's endpoints in the hash map.
After each build, update the global maximum if the new segment length is larger. Output the global maximum, which is the length of the longest contiguous segment so far.
Each build is processed in O(1) average time due to hash map operations. Overall O(n) time and O(n) space, where n is the number of builds.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Clarify the problem by confirming that the rating changes are applied sequentially and that the maximum rating includes the initial rating. Then, simulate the process in a single pass, tracking the current rating and the maximum seen so far, and return both values.
Pro tip: Mention that you can solve this in O(n) time and O(1) space, and that you would handle edge cases like an empty list of changes or all negative changes. Also, explicitly state that the maximum rating is updated after each change, including the initial rating.
Confirm that the rating changes are applied in order, that the initial rating is 1500, and that the maximum rating includes the starting rating. Ask if the changes can be positive, negative, or zero.
Initialize current_rating = 1500 and max_rating = 1500. These will track the rating after each change and the highest rating seen so far.
For each change in the sequence, update current_rating by adding the change. Then, if current_rating > max_rating, update max_rating to current_rating.
After processing all changes, return max_rating and current_rating as the final rating.
State that the time complexity is O(n) where n is the number of changes, and space complexity is O(1) since only two variables are used.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, clarify the problem with examples to ensure you understand the operation. Then, discuss a brute-force simulation and its inefficiencies, and propose an optimized approach using a stack or monotonic stack to compute the result in O(n) time. Finally, analyze time and space complexity and test with edge cases.
Pro tip: Mention that this problem is equivalent to computing the sum over each element of the minimum of the maximums of the left and right segments, which can be solved with a monotonic stack. This shows deep insight and can lead to a clean O(n) solution.
Restate the problem in your own words and walk through a small example to confirm the operation. Ask clarifying questions if needed.
Explain a straightforward simulation that repeatedly scans for the leftmost nonzero and performs subtractions. Analyze its time complexity (likely O(n^2)) and why it's inefficient.
Observe that the process is equivalent to summing, for each element, the minimum of the maximums of the left and right segments. Use a monotonic stack to compute these values efficiently.
Write clean code for the optimized solution, then test with edge cases like all zeros, single element, and increasing/decreasing arrays.
State the time and space complexity of the optimized solution (O(n) time, O(n) space) and compare with brute-force.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.